fix: mallavin derivates

Cargo.toml

@@ -1,6 +1,6 @@
 [package]
 name = "stochastic-rs"
-version = "0.10.3"
+version = "0.10.4"
 edition = "2021"
 license = "MIT"
 description = "A Rust library for quant finance and simulating stochastic processes."

src/stochastic/diffusion/cev.rs

@@ -50,10 +50,8 @@ impl Sampling<f64> for CEV {
         if i > 0 {
           stochastic_term[i] = self.sigma * self.gamma * cev[i].powf(self.gamma - 1.0) * gn[i - 1];
         }
-        malliavin[i] = self.sigma
-          * cev[i].powf(self.gamma)
-          * (det_term[i] + stochastic_term[i]).exp()
-          * (i as f64 * dt);
+        malliavin[i] =
+          self.sigma * cev[i].powf(self.gamma) * (det_term[i] + stochastic_term[i]).exp()
       }
 
       let _ = std::mem::replace(&mut *self.malliavin.lock().unwrap(), Some(malliavin));

src/stochastic/diffusion/gbm.rs

@@ -47,7 +47,7 @@ impl Sampling<f64> for GBM {
 
       // reverse due the option pricing
       for i in 0..self.n {
-        malliavin[i] = self.sigma * gbm.last().unwrap() * (i as f64 * dt);
+        malliavin[i] = self.sigma * gbm.last().unwrap();
       }
 
       // This equivalent to the following:

src/stochastic/volatility/heston.rs

@@ -91,17 +91,15 @@ impl Sampling2D<f64> for Heston {
               - self.kappa / 2.0)
               * ((self.n - i) as f64 * dt))
               .exp();
-            malliavin[i] =
-              (self.sigma * v.last().unwrap().sqrt() / 2.0) * det_term[i] * (i as f64 * dt);
+            malliavin[i] = (self.sigma * v.last().unwrap().sqrt() / 2.0) * det_term[i];
           }
           HestonPow::ThreeHalves => {
             det_term[i] = ((-(self.kappa * self.theta / 2.0 + 3.0 * self.sigma.powi(2) / 8.0)
               * v.last().unwrap()
               - (self.kappa * self.theta) / 2.0)
               * ((self.n - i) as f64 * dt))
               .exp();
-            malliavin[i] =
-              (self.sigma * v.last().unwrap().powf(1.5) / 2.0) * det_term[i] * (i as f64 * dt);
+            malliavin[i] = (self.sigma * v.last().unwrap().powf(1.5) / 2.0) * det_term[i];
           }
         };
       }

src/stochastic/volatility/sabr.rs

@@ -44,11 +44,10 @@ impl Sampling2D<f64> for SABR {
     #[cfg(feature = "malliavin")]
     if self.calculate_malliavin.is_some() && self.calculate_malliavin.unwrap() {
       // Only volatility Malliavin derivative is supported
-      let dt = self.t.unwrap_or(1.0) / (self.n - 1) as f64;
       let mut malliavin_of_vol = Array1::<f64>::zeros(self.n);
 
       for i in 0..self.n {
-        malliavin_of_vol[i] = self.alpha * v.last().unwrap() * (i as f64 * dt);
+        malliavin_of_vol[i] = self.alpha * v.last().unwrap();
       }
 
       let _ = std::mem::replace(